In this paper, we study a first order random coefficient autoregressive model with Laplace distribution as marginal. A random coefficient moving average model of order one with Laplace as marginal distribution is introduced and its properties are studied. By combining the two models, we develop a first order random coefficient autoregressive moving average model with Laplace marginal and discus...

in this paper, we consider admissible estimation of the parameter ?r in the gamma distribution with truncated parameter space under entropy loss function. we obtain the classes of admissible estimators. the result can be applied to estimation of parameters in the normal, lognormal, pareto, generalized gamma, generalized laplace and other distributions.

Microarrays allow the study of the expression profile of hundreds to thousands of genes simultaneously. These expressions could be from treated samples and the healthy controls. The Esscher transformed Laplace distribution is used to fit microarray expression data as compared to Normal and Laplace distributions. The Maximum Likelihood Estimation procedure is used to estimate the parameters of t...

The normal-Laplace (NL) distribution results from convolving independent normally distributed and Laplace distributed components. It is the distribution of the stopped state of a Brownian motion with normally distributed starting value if the stopping hazard rate is constant. Properties of the NL distribution discussed in the article include its shape and tail behaviour (fatter than the normal)...

In this paper we will investigate the semi-markov random processes with positive tendency, negative jumps and delaying boundary at zero in this article. The Laplace transform on time, Laplace-Stieltjes transform on phase of the conditional and unconditional distributions and Laplace-Stieltjes transform of the ergodic distribution are defined. The characteristics of the ergodic distribution will...

The method of Laplace transforms is used to find the distribution function, mean, and variance of the number of renewals of a renewal process whose inter-arrival time distribution has a rational Laplace transform. Where the Laplace transform is not rational, we use the Padé approximation method. We apply our method to certain examples and the results are compared to those reported by other rese...

It is often possible to e ectively calculate cumulative distribution functions and other quantities of interest by numerically inverting Laplace transforms. However, to do so it is necessary to compute the Laplace transform values. Unfortunately, convenient explicit expressions for required transforms are often unavailable. In that event, we show that it is sometimes possible to nd continued-fr...

AbstrAct: In this article, we introduce an alternative distribution , namely Esscher transformed Laplace distribution good enough to model the file size distribution of Web servers. It exhibits asymmetry, peakedness and tail heaviness, which are common features of file size data. Esscher transformed Laplace distribution belongs to one parameter regular exponential family. We derive their repres...

In a series of papers, we discussed the solution of Laplace’s differential equation (DE) by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC) of Riemann–Liouville fractional derivati...